Zeitschriftenartikel: „Music in mathematics“

1

Fernandez, Maria L. „Making Music with Mathematics“. Mathematics Teacher 92, Nr. 2 (Februar 1999): 90–97. http://dx.doi.org/10.5951/mt.92.2.0090.

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2

Perrine, Serge. „Mathematics and music. a diderot mathematical forum“. Mathematical Intelligencer 27, Nr. 3 (November 2005): 69–73. http://dx.doi.org/10.1007/bf02985844.

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3

Kitts, Roxanne. „Music and Mathematics“. Humanistic Mathematics Network Journal 1, Nr. 14 (1996): 23–29. http://dx.doi.org/10.5642/hmnj.199601.14.07.

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4

Boucher, Robert. „Music and Mathematics“. Journal of Humanistic Mathematics 5, Nr. 2 (Juli 2015): 174. http://dx.doi.org/10.5642/jhummath.201502.21.

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5

Behrends, Ehrhard. „Music and mathematics“. Mathematical Intelligencer 28, Nr. 3 (Juni 2006): 69–71. http://dx.doi.org/10.1007/bf02986890.

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6

Gangolli, Ramesh. „Music and Mathematics“. Perspectives of New Music 45, Nr. 2 (2007): 51–56. http://dx.doi.org/10.1353/pnm.2007.0001.

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7

DYER, JOSEPH. „The Place of Musica in Medieval Classifications of Knowledge“. Journal of Musicology 24, Nr. 1 (01.01.2007): 3–71. http://dx.doi.org/10.1525/jm.2007.24.1.3.

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ABSTRACT Medieval classifications of knowledge (divisiones scientiarum) were created to impose order on the ever-expanding breadth of human knowledge and to demonstrate the interconnectedness of its several parts. In the earlier Middle Ages the trivium and the quadrivium had sufficed to circumscribe the bounds of secular learning, but the eventual availability of the entire Aristotelian corpus stimulated a reevaluation of the scope of human knowledge. Classifications emanating from the School of Chartres (the Didascalicon of Hugh of St. Victor and the anonymous Tractatus quidam) did not venture far beyond Boethius, Cassiodorus, and Isidore of Seville. Dominic Gundissalinus (fl. 1144––64), a Spaniard who based parts of his elaborate analysis of music on Al-Fāārāābīī, attempted to balance theory and practice, in contradistinction to the earlier mathematical emphasis. Aristotle had rejected musica mundana, and his natural science left little room for a musica humana based on numerical proportion. Consequently, both had to be reinterpreted. Robert Kilwardby's De ortu scientiarum (ca. 1250) sought to integrate the traditional Boethian treatment of musica with an Aristotelian perspective. Responding to the empirical emphasis of Aristotle's philosophy, Kilwardby focused on music as audible phenomenon as opposed to Platonic ““sounding number.”” Medieval philosophers were reluctant to assign (audible) music to natural science or to place it among the scientie mechanice. One solution argued that music, though a separate subiectum suitable for philosophical investigation, was subalternated to arithmetic. Although drawing its explanations from that discipline, it nevertheless had its own set of ““rules”” governing its proper activity. Thomas Aquinas proposed to resolve the conflict between the physicality of musical sound and abstract mathematics through the theory of scientie medie. These stood halfway between speculative and natural science, taking their material objects from physical phenomena but their formal object from mathematics. Still, Thomas defended the superiority of the speculative tradition by asserting that scientie medie ““have a closer affinity to mathematics”” (magis sunt affines mathematicis) than to natural science.

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8

Chemillier, Marc. „Fourth Annual Mathematical Diderot Forum: Mathematics and Music“. Computer Music Journal 24, Nr. 3 (September 2000): 70–71. http://dx.doi.org/10.1162/comj.2000.24.3.70.

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9

Blackburn, Katie T., und David L. White. „Measurement, Mathematics, and Music“. School Science and Mathematics 85, Nr. 6 (Oktober 1985): 499–504. http://dx.doi.org/10.1111/j.1949-8594.1985.tb09654.x.

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10

Rosch, Paul J. „Music, medicine, and mathematics“. Stress Medicine 11, Nr. 1 (Januar 1995): 141–48. http://dx.doi.org/10.1002/smi.2460110124.

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11

Siddharthan, Rahul. „Music, mathematics and Bach“. Resonance 4, Nr. 3 (März 1999): 8–15. http://dx.doi.org/10.1007/bf02838719.

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12

Siddharthan, Rahul. „Music, mathematics and Bach“. Resonance 4, Nr. 5 (Mai 1999): 61–70. http://dx.doi.org/10.1007/bf02834321.

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13

Gorbunova, Irina B., und Mikhail S. Zalivadny. „Music, Mathematics and Computer Science: History of Interaction“. ICONI, Nr. 3 (2020): 137–50. http://dx.doi.org/10.33779/2658-4824.2020.3.137-150.

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The lecture “Music, Mathematics and Computer Science” characterizes by concrete examples various aspects of interaction of these studies with each other by incorporating the apparatus of corresponding scholarly disciplines (set theory, probability theory, information science, group theory, etc.). The role and meaning of these aspects in the formation of an integral perception about music and in the realization of practical creative musical goals are educed. Examination of these questions is what the lecture studies are devoted to as part of the educational courses “Mathematical Methods of Research in Musicology” and “Informational Technologies in Music” developed by the authors for the students of the St. Petersburg Rimsky-Korsakov State Conservatory and the Herzen State Pedagogical University of Russia. The lecture “Music, Mathematics and Computer Science” is subdivided into two parts. The fi rst part, “Music, Mathematics and Computer Science: History of Interaction” examines the processes of interconnection and interpenetration of various fi elds of music, mathematics and computer science, spanning the period from Ancient Times to the turn of the 20th and the 21st centuries. The second part of the lecture: “Music, Mathematics and Computer Science: Particular Features of Functioning of Computer-Musical Technologies” (due to be published in the journal’s next issue) is devoted to examining various aspects of developing and applying computer-musical technologies in contemporary musical practice, including musical composition, performance and the sphere of music education.

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14

Behrends, Ehrhard. „Mathematics and Music (Mathematical World, Vol. 28) by David Wright“. Mathematical Intelligencer 32, Nr. 4 (13.08.2010): 73–74. http://dx.doi.org/10.1007/s00283-010-9163-6.

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15

Fletcher, C. R., und J. Dieudonne. „Mathematics: The Music of Reason“. Mathematical Gazette 79, Nr. 484 (März 1995): 151. http://dx.doi.org/10.2307/3620029.

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16

Li, Hailong, Kalyan Chakraborty und Shigeru Kanemitsu. „Music as Mathematics of Senses“. Advances in Pure Mathematics 08, Nr. 12 (2018): 845–62. http://dx.doi.org/10.4236/apm.2018.812052.

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17

Giles, Rebecca M., und Jeannette Fresne. „Connecting music, movement, and mathematics“. Perspectives: Journal of the Early Childhood Music & Movement Association 11, Nr. 1 (01.06.2016): 22–25. http://dx.doi.org/10.1386/ijmec_0308_1.

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18

Haimson, Jennifer, Deanna Swain und Ellen Winner. „Do Mathematicians Have Above Average Musical Skill?“ Music Perception 29, Nr. 2 (01.12.2011): 203–13. http://dx.doi.org/10.1525/mp.2011.29.2.203.

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accompanying the view that music training leads to improved mathematical performance is the view that that there is an overlap between the kinds of skills needed for music and mathematics. We examined the popular conception that mathematicians have better music abilities than nonmathematicians. We administered a self-report questionnaire via the internet to assess musicality (music perception and music memory) and musicianship (music performance and music creation). Respondents were doctoral-level members of the American Mathematical Association or the Modern Language Association (i.e., literature and language scholars). The mathematics group did not exhibit higher levels of either musicality or musicianship. Among those reporting high music-performance ability (facility in playing an instrument and/or sight-reading ability), mathematicians did not report significantly greater musicality than did the literature/language scholars. These findings do not lend support to the hypothesis that mathematicians are more musical than people with nonquantitative backgrounds.

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19

Karlimah. „Elementary school students’ mathematical intelligence based on mathematics learning using classical music of the baroque era as the backsound“. SHS Web of Conferences 42 (2018): 00112. http://dx.doi.org/10.1051/shsconf/20184200112.

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Many studies suggest that classical music can inccrease the listeners’ intelligence, including mathematical intelligence [3, 12, 2, 11]. In this research, we used the classical music of Baroque era as the backsound during math learning. The research method used was quasi experiment with nonequivalent pretest-posttest control group design to grade V SD students in Tasikmalaya city. The results show that the use of classical music of Baroque era during the learning of mathematics gave a high contribution to the mathematical intelligence of fifth grade elementary school students. The student's mathematical intelligence can be seen in the cognitive abilities which were at the high level in the knowledge up to analysis, and at the low level in the synthesis and evaluation. Low mathematical intelligence was shown by students in calculating amount and difference of time, and projecting word problem into the form of mathematical problems. High mathematical intelligence arose in reading and writing integers in words and numbers. Thus, the mathematical intelligence of fifth grade Elementary School students will be better if classical music of Baroque era is used as the backsound in mathematics learning about solving math problems.

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20

Chao, Rocio. „Differences mathematics and music teaching-learning process between A Coruna and Lisbon“. New Trends and Issues Proceedings on Humanities and Social Sciences 2, Nr. 1 (28.06.2017): 93–98. http://dx.doi.org/10.18844/prosoc.v2i11.1908.

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21

Hughes, James R. „Mathematics and Music, by David Wright“. Journal of Mathematics and the Arts 5, Nr. 1 (März 2011): 43–48. http://dx.doi.org/10.1080/17513472.2010.551473.

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22

Montiel, Mariana, und Francisco Gómez. „Music in the pedagogy of mathematics“. Journal of Mathematics and Music 8, Nr. 2 (04.05.2014): 151–66. http://dx.doi.org/10.1080/17459737.2014.936109.

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23

Rings, Steven. „Journal of Mathematics and Music (review)“. Notes 64, Nr. 3 (2008): 548–50. http://dx.doi.org/10.1353/not.2008.0030.

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24

Shrestha, Sujan. „Mathematics Art Music Architecture Education Culture“. Nexus Network Journal 20, Nr. 2 (16.03.2018): 497–507. http://dx.doi.org/10.1007/s00004-018-0371-2.

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25

Talvila, Erik. „Folk Music Festivals and Mathematics Conferences“. Mathematical Intelligencer 37, Nr. 3 (03.07.2015): 39–40. http://dx.doi.org/10.1007/s00283-015-9561-x.

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26

Hudáková, Jana, und Eva Králová. „11. Creative Interdisciplinary Math Lessons by Means of Music Activities“. Review of Artistic Education 12, Nr. 2 (01.03.2016): 290–96. http://dx.doi.org/10.1515/rae-2016-0035.

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Abstract The goal of the paper is to introduce the project Comenius “EMP-Maths”, entitled ‘Providing Mathematics with Music Activities’, in which seven European countries took part. The key chapter is devoted to music activities that Slovak team integrated in the school subject of Mathematics. Music activities were selected and designed in accordance with the content of school subject Mathematics. To each particular theme the project solvers designed methodologies and didactic musical games, contests, music and drama exercises. The authoresses illustrate in detail one example of this integration which was presented during the meeting of 7 European countries in Barcelona in January 2015. Their illustration refers to interconnection of cognitive, affective, and psychomotor goals of both school subjects to develop musical and mathematical abilities of 11 – 12 year old elementary school pupils.

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27

Grandy, David. „The Musical Roots of Western Mathematics“. Journal of Interdisciplinary Studies 5, Nr. 1 (1993): 3–24. http://dx.doi.org/10.5840/jis199351/22.

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Alfred North Whtiehead stated that mathematics and music compete with each other for the honor of being the most novel achievement of the human imagination. Actually, there is no rivalry or competition, for the two enterprises interpenetrate once the investigation is pursued far enough. Though on opposite ends of the science-humanities spectrum, each discipline points toward the other and elicits the same sort of reverential puzzlement. This essay considers the seminal interconnection between music and mathematics and concludes that this unexpected conjunction of opposites bespeaks a higher, unseen reality. Music cum mathematics is an optics that allows us to discover, celebrate, and participate in God's ongoing Creation.

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28

Grandy, David. „The Musical Roots of Western Mathematics“. Journal of Interdisciplinary Studies 5, Nr. 1 (1993): 3–24. http://dx.doi.org/10.5840/jis199351/22.

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Alfred North Whtiehead stated that mathematics and music compete with each other for the honor of being the most novel achievement of the human imagination. Actually, there is no rivalry or competition, for the two enterprises interpenetrate once the investigation is pursued far enough. Though on opposite ends of the science-humanities spectrum, each discipline points toward the other and elicits the same sort of reverential puzzlement. This essay considers the seminal interconnection between music and mathematics and concludes that this unexpected conjunction of opposites bespeaks a higher, unseen reality. Music cum mathematics is an optics that allows us to discover, celebrate, and participate in God's ongoing Creation.

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29

Abdounur, Oscar João. „Mathematics and Music in Context: The Contribution of Erasmus Horicius to the Emergence of the Idea of Modern Number“. International Journal of Mathematical, Engineering and Management Sciences 1, Nr. 2 (01.09.2016): 62–67. http://dx.doi.org/10.33889/ijmems.2016.1.2-007.

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This article covers questions of how the relationship between mathematics and theoretical music throughout western history shaped modern comprehension of critical notions such as “ratio” and “proportion”. In order to do that, it will be consider a procedure taken by Erasmus of Höritz, a Bohemian mathematician and music theorist who emerged in the early 16th century as a German humanist very articulate with musical matters. In order to divide the tone, Erasmus preferred to use a numerical method to approach the geometrical mean, although he did not recognize his procedure itself as an approximation of the true real number value of the geometric mean. The Early Modern Period saw the growing use of geometry as an instrument for solving structural problems in theoretical music, a change not independently from those occurred in the conception of ratio/number in the context of theoretical music. In the context of recovery of interest in Greek sources, Erasmus communicated to musical readers an important fruit of such a revival and was likely the first in the Renaissance to apply explicitly Euclidean geometry to solve problems in theoretical music. Although Erasmus also considered the tradition of De institutione musica of Boethius, he was based strongly on Euclid’s The Elements, using geometry in his De musica in different ways in order to solve musical problems. It is this comprehensive geometrical work rather than the summary arithmetical and musical books of Boethius that serves Erasmus as his starting-point. However, Erasmus proposed a proportional numerical division of the whole tone interval sounding between strings with length ratio of 9:8, since it was a primary arithmetical problem. This presentation aims at showing the educational potentiality of the implications of such a procedure of Erasmus on the transformation of conception of ratio and on the emergence of the idea of modern number in theoretical music contexts. Under a broader perspective, it aims at show the implications on education of a historical/epistemological and interdisciplinary appraisal of theoretical music and mathematics.

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30

Johnson, Gretchen L., und R. Jill Edelson. „Integrating Music and Mathematics in the Elementary Classroom“. Teaching Children Mathematics 9, Nr. 8 (April 2003): 474–79. http://dx.doi.org/10.5951/tcm.9.8.0474.

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Increasingly, teachers are being encouraged to engage in interdisciplinary instruction. Although many of us are comfortable using children's literature as the basis for interdisciplinary units, we rarely think to integrate mathematics and music in our lessons. Music actively involves students in learning and helps develop important academic skills (Rothenberg 1996). By using music to enhance children's enjoyment and understanding of mathematics concepts and skills, teachers can help children gain access to mathematics through new intelligences (Gardner 1993). This integration is especially effective with children who have strong senses of hearing and musical intelligence.

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31

Anindita Roy Chowdhury und Naresh Sharma. „Scientific Numerical Pattern in Stringed-Fretted Musical Instrument“. Mathematical Journal of Interdisciplinary Sciences 8, Nr. 2 (30.03.2020): 69–74. http://dx.doi.org/10.15415/mjis.2020.82009.

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Music, a creative art has a strong foundation on science and mathematics. Source of music can vary from vocal chord to various types of musical instruments. One of the popular stringed and fretted musical instrument, the guitar has been discussed here. The structure of the guitar is based on mathematical and scientific concepts. Harmonics and frequency play pivotal role in generation of music from a guitar. In this paper, the authors have investigated various factors related to the structure of a guitar. Aspects related to the musical notes of a guitar have been analyzed to gain a better insight into the mathematical pattern involved in the music of a guitar.

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32

Shere, Charles, Iannis Xenakis, Sharon Kanach und Nouritza Matossian. „Formalized Music: Thought and Mathematics in Composition“. Notes 50, Nr. 1 (September 1993): 96. http://dx.doi.org/10.2307/898697.

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33

Rowe, Robert. „Mathematics and music: composition perception and performance“. Journal of Mathematics and the Arts 8, Nr. 3-4 (22.04.2014): 138. http://dx.doi.org/10.1080/17513472.2014.909125.

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34

Rothstein, Edward. „The Inner Life of Music and Mathematics“. Math Horizons 3, Nr. 2 (November 1995): 6–8. http://dx.doi.org/10.1080/10724117.1995.11974947.

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35

Cuomo, Salvatore, Ardelio Galletti und Gabriele Guerriero. „An interdisciplinary laboratory in mathematics and music“. Applied Mathematical Sciences 8 (2014): 6709–16. http://dx.doi.org/10.12988/ams.2014.49685.

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36

Gorbunova, Irina B. „Music, Mathematics and Computer Science: Features of Functioning of Computer-Musical Technologies“. ICONI, Nr. 1 (2021): 137–47. http://dx.doi.org/10.33779/2658-4824.2021.1.137-147.

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The lecture “Music, Mathematics and Computer Science” is subdivided into two parts. The fi rst part, “Music, Mathematics and Computer Science: History of Interaction” (see ICONI journal, No. 3, 2020) examines the processes of interconnection and interpenetration of various fi elds of music, mathematics and computer science, spanning the period from Ancient Times to the turn of the 20th and 21st centuries. The second part of the lecture: “Music, Mathematics and Computer Science: Particular Features of Functioning of Computer-Musical Technologies” is devoted to examining various aspects of developing and applying computer-musical technologies in contemporary musical practice, including musical composition, performance and the sphere of music education

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37

Keren-Sagee, Alona. „JOSEPH SCHILLINGER – A DISCIPLE'S REMINISCENCES OF THE MAN AND HIS THEORIES: AN INTERVIEW WITH PROF. ZVI KEREN“. Tempo 64, Nr. 251 (Januar 2010): 17–27. http://dx.doi.org/10.1017/s0040298210000033.

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Joseph Schillinger (1895–1943), the eminent Russian-American music theorist, teacher and composer, emigrated to the United States in 1928, after having served in high positions in some of the major music institutions in the Ukraine, Khar'kov, Moscow, and Leningrad. He settled in New York, where he taught music, mathematics, art history, and his theory of rhythmic design at the New School for Social Research, New York University, and the Teachers College of Columbia University. He formulated a philosophical and practical system of music theory based on mathematics, and became a celebrated teacher of prominent composers and radio musicians. Schillinger's writings include: Kaleidophone: New Resources of Melody and Harmony (New York: M. Witmark, 1940; New York: Charles Colin, 1976); Schillinger System of Musical Composition, 2 vols. (New York: Carl Fischer, 1946; New York: Da Capo Press, 1977); Mathematical Basis of the Arts (New York: Philosophical Library, 1948; New York: Da Capo Press, 1976); Encyclopedia of Rhythms (New York: Charles Colin, 1966; New York: Da Capo Press, 1976).

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38

Kravanja, Peter. „Music: A mathematical offering“. Mathematical Intelligencer 30, Nr. 1 (März 2008): 76–77. http://dx.doi.org/10.1007/bf02985765.

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39

DÜPPE, TILL. „Listening to the Music of Reason: Nicolas Bourbaki and the Phenomenology of the Mathematical Experience“. PhaenEx 10 (25.10.2015): 38–56. http://dx.doi.org/10.22329/p.v10i0.3935.

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Jean Dieudonné, the spokesman of the group of French mathematicians named Bourbaki, called mathematics the music of reason. This metaphor invites a phenomenological account of the affective, in contrast to the epistemic and discursive, nature of mathematics: What constitutes its charm? Mathematical reasoning is described as a perceptual experience, which in Husserl’s late philosophy would be a case of passive synthesis. Like a melody, a mathematical proof is manifest in an affective identity of a temporal object. Rather than an exercise for its own sake, this account sheds a different light on both the epistemic limitation of mathematical science, and the discursive problem of social responsibility in mathematics – two issues at the heart of Husserl’s critique of science as well as of mid-20th century mathematics, for which Nicolas Bourbaki stands as a monument of rigor.

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40

Abu Bakar, Kamariah, und Mohamad Azam Samsudin. „Teaching Young Children Early Mathematics through Music and Movement“. International Journal of Learning, Teaching and Educational Research 20, Nr. 5 (30.05.2021): 271–81. http://dx.doi.org/10.26803/ijlter.20.5.15.

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The purpose of this study was to explore the integration of music and movement elements into young children’s mathematics classrooms. Using a qualitative approach, this research was a case study. Three teachers were purposely selected as participants for this study. The teachers were interviewed to gain information about the songs and movements they chose to employ into their instruction. Additionally, their lessons were observed to attain the ways they incorporated music and movement. These sessions were video recorded to gain a rich picture of the songs and movements incorporated as well as the benefits of such practice in the teaching and learning of mathematics. The findings from the interviews (with teachers), classroom observations, and photographs exhibited that the teachers used familiar, easy and simple songs to be incorporated in their instruction. It was also evident that embedding music and movement activities into young children's mathematics lessons had a positive impact on the students' learning of early mathematics. The students focused on what the teachers were doing and repeating after them. This enhanced their mathematics learning. The implication of this study is that mathematics instruction should be employed in a fun yet meaningful way by incorporating music and movement activities as teaching and learning activities. More importantly, is that children learn mathematics with understanding.

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41

Husson, Matthieu. „Deux exemples d’utilisation des mathématiques en musique dans le premier quatorzième siècle latin“. Early Science and Medicine 15, Nr. 4-5 (2010): 448–73. http://dx.doi.org/10.1163/157338210x516288.

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This article analyses the conditions under which mathematics could enter the field of fourteenth-century music. It distinguishes between descriptive and argumentative uses of mathematics. Jean de Murs’ uses of arithmetic to study musical time is an example of the former, Jean de Boen’s study of the division of the whole tone an example of the latter. It is furthermore explained how the mathematical descriptions appear to bring into agreement two types of constraint, namely the physical characteristics of sound and the aesthetic principles of the medieval discourse about music. Within these constraints, mathematics manages to fulfill different argumentative roles: it has an ontological function when music is seen as a part of the quadrivium; but an explicative function in the framework of the scientia media and, in an more innovative spirit for Jean de Boens, it provides a definition of the possible in the argumentation about the division of the whole tone.

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42

Latinčić, Dragan. „Possible principles of mathematical music analysis“. New Sound, Nr. 51 (2018): 153–74. http://dx.doi.org/10.5937/newso1851153l.

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The text is a summary of many years of research in the domains of micro-intervals, metric-rhythmic projection of the spectrum harmonics, and the establishment of a link with mathematics, more precisely, geometry, with a special focus on the application of the Pythagorean Theorem. Mathematical music analysis enables the establishment of methods for constructing right, obtuse, and acute musical triangles as well as projections of their edges (sides), which are recognized in trigonometry as the functions of angles: the sine, cosine, and so on; as well as the establishment of methods for constructing spectral and scalar (intonative-temporal) trigonometric unit circles with their function graphs.

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43

Nita, Bogdan G., und Sajan Ramanathan. „Fluids in Music: The Mathematics of Pan’s Flutes“. Fluids 4, Nr. 4 (10.10.2019): 181. http://dx.doi.org/10.3390/fluids4040181.

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We discuss the mathematics behind the Pan’s flute. We analyze how the sound is created, the relationship between the notes that the pipes produce, their frequencies and the length of the pipes. We find an equation which models the curve that appears at the bottom of any Pan’s flute due to the different pipe lengths.

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44

Wardhaugh, Benjamin. „The Logarithmic Ear: Pietro Mengoli's Mathematics of Music“. Annals of Science 64, Nr. 3 (13.06.2007): 327–48. http://dx.doi.org/10.1080/00033790701303239.

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45

Cohen, H. Floris. „Music, Experiment and Mathematics in England, 1653–1705“. Journal of Mathematics and Music 4, Nr. 3 (November 2010): 173–74. http://dx.doi.org/10.1080/17459737.2010.513277.

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46

Wiggins, Geraint A. „Music, mind and mathematics: theory, reality and formality“. Journal of Mathematics and Music 6, Nr. 2 (Juli 2012): 111–23. http://dx.doi.org/10.1080/17459737.2012.694710.

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47

Field, J. V. „Renaissance mathematics: diagrams for geometry, astronomy and music“. Interdisciplinary Science Reviews 29, Nr. 3 (September 2004): 259–77. http://dx.doi.org/10.1179/030801804225018873.

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Cohen, Floris. „Music, Experiment and Mathematics in England (1653-1705)“. Early Science and Medicine 15, Nr. 3 (2010): 310–12. http://dx.doi.org/10.1163/157338210x494049.

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Papadopoulos, Athanase. „Mathematics and music theory: From pythagoras to rameau“. Mathematical Intelligencer 24, Nr. 1 (Dezember 2002): 65–73. http://dx.doi.org/10.1007/bf03025314.

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Tokhmechian, Ali, und Minou Gharehbaglou. „Music, Architecture and Mathematics in Traditional Iranian Architecture“. Nexus Network Journal 20, Nr. 2 (26.05.2018): 353–71. http://dx.doi.org/10.1007/s00004-018-0381-0.

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